On recycling the peanut butter jar...

OK, so I've been recycling for years and I'm a huge supporter. I even break down my items and sort everything out according to the town's instructions. Anything I can do to help maintain (or even better) the environment I'm all for it. There is, however, one item of recycling that always causes me inner turmoil. The peanut butter jar. One one hand, I don't want to put any food wastes into the recycling, so everything gets rinsed out before going in the bin. On the other hand, I expend so much effort and hot water trying to get the last of the peanut butter out of the jar that I feel like I'm wasting far more than I'm saving. At what point does it become not worth the effort? Should I just toss the nearly-empty jar into the trash and let it take up space? Should I casually leave the jar open and within reach of the dog, and then just recycle whatever parts of it he fails to digest? The town's instruction booklet doesn't offer me any help on this one...